Birkhoff系统的守恒量与稳定性

利用Birkhoff系统的守恒量来研究系统的稳定性.如果守恒量的组合能够成为Liapunov函数，便可用来研究系统的平衡稳定性和运动稳定性. 关键词： Birkhoff系统 守恒量 Liapunov稳定性     

A connection theory for a nonlinear differential constrained system

An Ehresmann connection on a constrained state bundle defined by nonlinear differential constraints is constructed for nonlinear nonholonomic systems. A set of differential constraints is integrable if and only if the curvature of the Ehresmann connection vanishes. Based on a geometric interpretation of d－δ commutation relations in constrained dynamics given in this paper, the complete integrability conditions for the differential constraints are proven to be equivalent to the three requirements upon the conditional variation in mechanics: (1) the variations belong to the constrained manifold; (2) the time derivative commutes with variational operator; (3) the variations satisfy the Chetaev's conditions.     

变质量完整力学系统的非Noether守恒量

利用时间不变的无限小变换下的Lie对称性,研究变质量完整力学系统的一类新的守恒量.给出系统的运动微分方程,研究时间不变的无限小变换下的Lie对称性确定方程,将Hojman定理推广并应用于这类系统 关键词： 变质量系统 完整约束 确定方程 非Noether守恒量